a large birdcage has the shape of a rectangular prism. a straight branch of length b (in meters) is placed…
a large birdcage has the shape of a rectangular prism. a straight branch of length b (in meters) is placed in the cage going from one corner to the opposite corner as shown in the figure. (the figure is not drawn to scale.) (a) find a. a = m (b) use your answer to part (a) to find b, the length of the branch. round your answer to the nearest tenth of a meter. b = m
Answer
Explanation:
Step1: Find the diagonal of the base
The base is a square with side - length 6m. Using the Pythagorean theorem for the base, if the side - lengths of the base are (x = 6m) and (y = 6m), the diagonal of the base (d) is given by (d=\sqrt{6^{2}+6^{2}}). [d=\sqrt{36 + 36}=\sqrt{72}=6\sqrt{2}\text{ m}]
Step2: Find the length from one corner to the opposite corner of the rectangular prism
The height of the prism (h = 7m), and we want to find the length (b) (the space - diagonal of the rectangular prism). Using the three - dimensional Pythagorean theorem (b=\sqrt{d^{2}+h^{2}}), where (d = 6\sqrt{2}\text{ m}) and (h = 7m). First, (d^{2}=(6\sqrt{2})^{2}=72) and (h^{2}=49). Then (b=\sqrt{72 + 49}=\sqrt{121}=11\text{ m})
Answer:
11 m